Consider a second-order system whose transfer function is in standard form as in Equation 10.7. Assume that the requirements for the system unit-step response are rise time \(t_{\mathrm{r}} \leq 0.1 \mathrm{~s}\), overshoot \(M_{\mathrm{p}} \leq 20 \%\), and \(2 \%\) settling time \(t_{\mathrm{s}} \leq 2 \mathrm{~s}\). Sketch the allowable region for the poles in the \(s\)-plane.

Y(s) U(s) co s+250s+ 2 (10.7)